time value Math problems?
Please help me! I am having trouble solving these problems. I keep trying different calculations but nothing works and the book is no help at all.
1. How much will you have at the end of 5 years in a European vacation account if you deposit $200 a month in an account that is paying a nominal 12 percent per year, compounded monthly?
2. Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter?
1. Firstly i’ll be w0rking in m0nths so will use the effective monthly interest rate which is 1% effective per month.
At the end of five years the accumulated amount=
200(1+0.01)^59+200(1+0.01)^58+…..+200(1+0.01)
=200 ( ( (1.01)^60-1) )/0.01
=200(81.66966986)
=$16333.93
2.At time 10
You would expect X to accumulate to $180 000
Thus you have
180000=X( (1.08)^4-1)/0.08))(1.10)^6 + X ((1.10)^6-1)/0.10)
Solving for X you get X= $7487.78
Note that i summed up the payments similarly to No.1 only that these payments were made yearly and i summed up payments of X for the first 4 years then brought it to time 10 at the interest rate of 10% and summed up the remaining payments for the 6years at the applicable 10%.The main objective is bringing evrything to the same time ( in this case time 10) at the interest rates which apply.
Also if you know the appropriate accumulating formulas they are simpler to use.
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